Is "meet" an appropriate abbreviation for "meeting"?

​Meet as a noun refers to sports events, if you are referring to business or social gatherings you should use "meeting":

• (us) a sports event: a track/swim meet the first meet of the season ​
• (uk) an occasion when people go fox hunting

Cambridge Dictionary

Not in a business setting, which I assume you mean by the fact that you're talking about a project. Sometimes meetings are called meets, but this is usually done to be cheeky. And such a meet is never a formal meeting, but a less formal social encounter or gathering (e.g. "meet and greet"). (Or, as JOSH points out, a sporting event.) In a business setting, one would never say "I'm headed to my 9 AM status meet."